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Transcript
Basic Kinetic Concepts • Inertia: – Natural property of a body to resist a change in state of motion (i.e., state of motion defined by velocity, ∆ state of motion = acceleration) Newton’s 1st Law: Inertia • A body will stay at rest... • A body will continue to move with the same velocity unless... • A net force acts on the body – e.g., to speed up or slow down an object’s motion, and/or to change an object’s direction of motion, and object’s inertia must be overcome. 1 Mass • Quantity of matter of which a body is composed (a measure of “stuff”) • Direct measure of a body’s resistance to change in linear motion – e.g., it is more difficult to change the motion of a large object (large mass) than a small object – large mass (e.g., shot) vs. small mass (e.g., tennis ball). Which requires more effort (i.e., force)? Definitions • Force: – Effect of one body on another – A push or a pull applied to an object – That which is needed to change the state of motion (i.e., velocity) of an object • Acceleration: – Rate of change of velocity of an object with respect to time. • Describes the change in state of motion of an object (i.e., ∆ velocity) 2 Newton’s 2nd Law: ΣF = ma ΣF = “Net force” = Sum of all forces m = mass (a measure of inertia) a = linear acceleration Example • What average net force must a baseball catcher apply to an 80 mph (35.8 m/s) pitch to stop it over a time of .025 s? (mass = 4.5 oz = 0.13 kg) – Know: m = .13 kg; t = 0.025 s; vi = 35.8 m/s; vf = 0 m/s – Need: F – Use: F = ma ...but…we must find a first and a = (vf – vi)/t – Answer: F = ma = 0.13 kg × (0 m/s – 35.8 m/s )/0.025 s = –186.2 N 3 • Things to consider: – The meaning of a negative force – Average v. instantaneous force – The effect of ∆t on F • Important interpretations of the ΣF = ma relationship: – Cause (ΣF) and effect (a) relationship: the most important concept in this class! • a directly proportional to and in the same direction as ΣF • To produce a given a, it takes a larger ΣF for a more massive object Newton’s 3rd Law: Action/Reaction • Action-reaction: describes how objects interact with one another. – If one body exerts a force on a second body, the second exerts back on the first a force of equal magnitude but opposite direction – example: Vertical jumping • “Action” force is applied by person (via muscles) and acts on ground. • “Reaction” force is applied by ground and acts on person. 4 Newton’s Law of Gravitation • A fundamental physical principle that describes the concept of gravity... • Any two particles of matter (any objects or bodies) attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them (i.e., distance between their centers). F = G⋅ ( m1 ⋅ m2 ) l2 G = gravitational constant = 6.7 x 10-11 N⋅m2/kg2 • Like it or not, there is a force of attraction between you and the person sitting next to you. – However, this force is so small that you don’t notice it. – When one of the objects is the earth (with its huge mass), the force of attraction (i.e. gravity) is very significant. Example F = G ⋅ (m ⋅m 1 • Two students sitting 1.5 m apart ( ) F = 6.7 x10-11 N ⋅ m2 / kg 2 ⋅ l 2 ) 2 ( 70 kg )(50 kg ) (1.5m) 2 F = 10422 x10 −11 = 1.04 x10 − 7 N • Attraction between earth and student ( ) F = 6.7 x10-11 N ⋅ m2 / kg 2 ⋅ (5.98 x1024 kg )(50 kg ) (6.38 x106 m) 2 F = 4.92 x101 = 491 N 5 Weight • Question: Is earth’s gravitational attraction the same for all objects on or near the earth’s surface? • Answer: NO...this force is dependent on the involved masses and the distance between the CM of the object and the CM of the earth. Weight vs. Mass • Are weight and mass the same thing? NO (Why or why not) – An objects weight represents the force of attraction between the earth and the object. Mass represents the quantity of matter or stuff of which a body is composed. • Simplified relationship for the link between weight and mass on earth: W = mg where g = G ⋅ m e a r th 2 l 6